Fun with Fundamentals Puzzler: Free for ball

Every November, fans gather for the Otheta State vs. Cactus U match-up. This year, it's late in the first quarter — third and ten — and OSU's Johnny T. Jectrie fades back to pass. He lays out a tight spiral, but a Cactus rascal deflects the ball at the line of scrimmage — imparting an end-over-end tumble to the ball's motion.

If the ball's spin is directed as shown as it tumbles towards one very tightly covered receiver, and it's gyrating at Ψ = 4 rad/sec, what is its angular velocity?

Assume that the ball's ratio of axial to transverse moments of inertia is one third, measured with respect to the center of mass.